At this point, I don't think that the observer is from a parallel universe. Or, more specifically, that he isn't a human from a parallel universe. At this point, I think he's something from outside the system, observing events, and perhaps setting them in motion by observing them.
I do have a silly theory that's probably wrong.
I'm thinking of Schrodinger's Cat. A subatomic particle exists as a superposition of states until it is observed, at which point the quantum waveform collapses into a single randomly determined state.
Let's say that the universes aren't truly parallel, but are, in fact, a single universe that exists as a quantum superposition of all the universe. Each quantum state thus appears to be a separate universe, but all exist in the same space-time and are composed of the same matter and energy.
The enhanced perceptional abilities granted by cortexifan allow the soldiers to perceive all the different quantum states of all matter in the universe and to choose between them on a subatomic scale, thus producing improbable effects such as spontaneous human combustion.
The Observer then, Observes. The act of observation initiates a quantum waveform collapse, the scale of which depends on the scale of the observation. Eventually, this will cause allparitcles in the universe to setle into a single stable quantum state, effectivly destroying all other realities.
The Cortexifan treatments allow the Soldiers to mediate this waveform collapse, they can select quantum state that they prefer rather than leaving it to random chance.